Libraries¶

In [1]:
# import libraries 
import numpy as np
import scipy as sp
import networkx as nx
import matplotlib.pyplot as plt

Parameters¶

In [2]:
# Create an empty graph
G = nx.Graph()

# Add nodes
nodes = range(1, 17)
G.add_nodes_from(nodes)

# Add edges based on the visual structure
edges = [
    (1, 2), (1, 3), (1, 4), (2, 4), (2,5), (3, 4), (3, 6), (3, 7), (3, 8), (4, 5), (4, 8), (4, 9),
    (5, 9), (6, 7), (7, 8), (7, 11), (7, 10), (7, 13), (8, 9), (8, 11), (8, 12), (9, 12),
    (10, 13), (11, 12), (11, 13), (11, 14), (12, 14), (12, 15), (13, 14), (13, 16) ,(14, 15),
    (14, 16), (15, 16)
]
G.add_edges_from(edges)

# Set parameters
alpha = 0.0050415
beta = 0.000013047
delta = 0.0079639
do = 0.0017783
numerator = 2 * delta**2 * beta + do * (alpha + beta)**2 + 2 * (alpha + beta) * delta * np.sqrt(2 * do * (alpha + beta))
denominator = 2 * alpha * delta**2
Ic = numerator / denominator
I = Ic + 0.1

# Critical eigenvalue, must be 1.19198455
lambda_c = (do * (alpha + beta)**2 + 2 * beta * delta**2 - 2 * I * alpha * delta**2) / (4 * do * delta * (alpha + beta))

# Compute the homogeneous steady states
rho_ss = alpha * delta / (alpha + beta)
O_ss = (alpha + beta) / delta
params = {
    'alpha': alpha,
    'beta': beta,
    'delta': delta,
    'do': do,
    'I': I,
    'rho_ss': rho_ss,
    'O_ss': O_ss,
    'lambda_c': lambda_c
}
In [3]:
params
Out[3]:
{'alpha': 0.0050415,
 'beta': 1.3047e-05,
 'delta': 0.0079639,
 'do': 0.0017783,
 'I': np.float64(0.7074034423516578),
 'rho_ss': 0.007943343261028139,
 'O_ss': 0.6346823792363039,
 'lambda_c': np.float64(-1.415470896407335)}

Dispertion Relation¶

In [6]:
def dispertion_relation(params, plot=False):
    """
    Function to get the dispersion relation of the graph
    """
    # Parameters
    alpha = params['alpha']
    beta = params['beta']
    delta = params['delta']
    do = params['do']
    I = params['I']
    rho_ss = params['rho_ss']
    O_ss = params['O_ss']
    lambda_c = params['lambda_c']
    
        # Define a suitable range of lambda values
    lambda_vals = np.linspace(-8, 0, 500)

    # b(λ)
    def b(lambda_N):
        return ((alpha + beta)/delta
                + (delta * beta)/(alpha + beta)
                - lambda_N * (2 + do))

    # c(λ)
    def c(lambda_N):
        return (
            2 * do * (lambda_N**2)
            + lambda_N * (
                (2 * I * alpha * delta) / (alpha + beta)
                - (2 * delta * beta) / (alpha + beta)
                - (do * (alpha + beta)) / delta
            )
            + (alpha + beta)
        )

    # η(λ) = -b(λ)/2 + (1/2)*sqrt(b(λ)^2 - 4 c(λ))
    def eta(lambda_N):
        return -0.5 * b(lambda_N) + 0.5 * np.sqrt(b(lambda_N)**2 - 4 * c(lambda_N))

    # Evaluate eta on the grid of lambda values
    eta_vals = eta(lambda_vals)

    # Extract only the real part
    eta_vals_real = np.real(eta_vals)

    # Determine the range for positive values
    positive_range = np.where(eta_vals_real > 0)[0]

    min_lambda = lambda_vals[positive_range[0]]
    max_lambda = lambda_vals[positive_range[-1]]

    if plot: 
        # Plot the real part of eta vs. lambda
        plt.figure()
        plt.plot(lambda_vals, eta_vals_real, label=r'Real[$\eta(\lambda)$]')
        # Graph a horizontal line at 0
        plt.axhline(0, color='black', linestyle='-')
        plt.xlabel(r'$\lambda$')
        plt.ylabel(r'Real[$\eta(\lambda)$]')
        plt.title('Plot of Real($\eta(\lambda)$) vs. $\lambda$')
        plt.legend()
        plt.grid(True)
        plt.show()

    return {
        'min_lambda': float(min_lambda),
        'max_lambda': float(max_lambda),
    }

    
In [7]:
dispertion_relation(params)
Out[7]:
{'min_lambda': -2.1643286573146296, 'max_lambda': -0.6573146292585177}

Dynamics¶

In [9]:
# Set of functions



def get_dynamics(graph, params, plot=False):
    """
    Function to get the dynamics of the graph
    """
    # Parameters
    alpha = params['alpha']
    beta = params['beta']
    delta = params['delta']
    do = params['do']
    I = params['I']
    rho_ss = params['rho_ss']
    O_ss = params['O_ss']
    lambda_c = params['lambda_c']
    G = graph
    n = G.number_of_nodes()
    e = G.number_of_edges()
    A = nx.adjacency_matrix(G).todense()

    
    def system(t, y, A, alpha, beta, delta, do, I):
        """
        y[k][0] is rho
        y[k][1] is O
        n repetitions for each municipality
        2 variables, rho and O
        """


        y = y.reshape(n, 2)
        
        dydt = np.zeros_like(y)

        

        def function_1(j):
            return A[i][j] * (y[j][0] - y[i][0])
        
        def function_2(j):
            return A[i][j] * ((y[i][1]/y[j][1])**I * y[j][0] - (y[j][1]/y[i][1])**I * y[i][0])
        
        def function_3(j):
            return A[i][j] * (y[j][1] - y[i][1])
        
        j = np.arange(16)
        

        for i in range(n):
            f_1_j = np.vectorize(function_1)(j)
            f_2_j = np.vectorize(function_2)(j)
            f_3_j = np.vectorize(function_3)(j)
            dydt[i, 0] = -y[i, 0] * y[i, 1] + alpha + np.sum(f_1_j) + np.sum(f_2_j)
            dydt[i, 1] = -delta * y[i, 1] + beta + y[i, 0] * y[i, 1] + do * np.sum(f_3_j)

        return dydt.flatten()
    # Initial conditions
    np.random.seed(0)
    y0 = np.random.uniform(0.01, 2, n * 2)

    # Time span
    t_span = (0, 1000)
    t_eval = np.linspace(*t_span, 100)

    # Solve the system of ODEs
    print("Starting the integration...")
    solution = sp.integrate.solve_ivp(system, t_span, y0, method='BDF', args=(A, alpha, beta, delta, do, I), t_eval=t_eval)
    print("Integration finished.")

    t = solution.t
    y = solution.y.reshape(n, 2, -1)

    # Extract the stationary state from the dynamics (the last values)
    nodes = np.arange(1, n + 1)
    last_values_rho = np.zeros(n)
    last_values_O = np.zeros(n)
    for i in range(n):
        last_values_rho[i] = y[i, 0][-1]
        last_values_O[i] = y[i, 1][-1]

    print("Linear algebra computations...")
    # Computing the spectrum of the Laplacian matrix
    L = -1 * nx.laplacian_matrix(G).todense()

    eigenvalues, eigenvectors = np.linalg.eig(L)

    # get the index of the nearest eigenvalue to lambda_c
    index_lambda_c = np.argmin(np.abs(eigenvalues - lambda_c))
    # the index cannot be zero 
    min_lambda, max_lambda = dispertion_relation(params).values()
    # check if the index is in the range
    critical_eigenvalue = eigenvalues[index_lambda_c]
    linear_analysis = True
    
    if critical_eigenvalue < min_lambda or critical_eigenvalue > max_lambda:
        linear_analysis = False
    
    if linear_analysis:
        critical_eigenvector = eigenvectors[:, index_lambda_c]
    else: 
        critical_eigenvector = np.zeros(n)
        print("The critical eigenvalue is not in the range of the dispersion relation.")
        print("The linear analysis cannot be performed.")
        print("The critical eigenvalue is: ", critical_eigenvalue)

    

    if plot:
        
        # Creating the stem plots
        fig, axes = plt.subplots(3, 1, figsize=(10, 10))

        axes[0].stem(nodes, last_values_rho, linefmt='gray', markerfmt='ko', basefmt=' ', bottom=rho_ss)
        axes[0].axhline(rho_ss, color='red', linestyle='--')


        # Labeling the axes
        axes[0].set_xlabel('Nodes')
        axes[0].set_ylabel('rho')

        axes[1].stem(nodes, last_values_O, linefmt='gray', markerfmt='ko', basefmt=' ', bottom=O_ss)
        axes[1].axhline(O_ss, color='red', linestyle='--')

        # Labeling the axes
        axes[1].set_xlabel('Nodes')
        axes[1].set_ylabel('O')

        axes[2].stem(nodes, critical_eigenvector, linefmt='gray', markerfmt='ko', basefmt=' ')
        axes[2].axhline(0, color='red', linestyle='--')

        # Labeling the axes
        axes[2].set_xlabel('Nodes')
        axes[2].set_ylabel('eigenvector')

        # Display the plot
        plt.show()

    # Variance 
    variance_rho = np.var(last_values_rho)
    variance_O = np.var(last_values_O)
    variance_eigenvector = np.var(critical_eigenvector)

    # Inverse Participation Ratio (IPR)
    ipr_rho = np.sum(last_values_rho**4) / (np.sum(last_values_rho**2)**2)
    ipr_O = np.sum(last_values_O**4) / (np.sum(last_values_O**2)**2)
    ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)

    # Network average degree
    k_avg = 2 * e / n

    print("Computations finished.")
    
    



    # Return the results
    return {
        'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
        'last_values_rho': last_values_rho.tolist(),
        'last_values_O': last_values_O.tolist(),
        'critical_eigenvector': critical_eigenvector.tolist(),
        'eigenvalues': eigenvalues.tolist(),
        'variance_rho': float(variance_rho),
        'variance_O': float(variance_O),
        'variance_eigenvector': float(variance_eigenvector),
        'ipr_rho': float(ipr_rho),
        'ipr_O': float(ipr_O),
        'ipr_eigenvector': float(ipr_eigenvector),
        'k_avg': float(k_avg),
    }
        


        


    

Experiments¶

In [6]:
# Create the experiments

def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
    print("Starting the experiments...")
    transitivity = []
    average_path_length = []
    p_values = np.logspace(-4, 0, n_experiments)
    small_world_graphs = []

    # List that will contain the dynamics of the graphs
    dynamics_data = {}
    # Max clustering coefficient
    max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
    # Max length
    max_length = n_nodes / (2 * n_neighbors)

    # Compute the transitivity and average length path for each graph
    for i, p in enumerate(p_values):
        print(f"Computing graph {i + 1}/{n_experiments}...")
        small_world_graphs = []
        transitivities = []
        avg_lenghts = []
        dynamics = []
        print("Computing samples...")
        for seed in range(sample_size):
            small_world_graphs.append(nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed))
        print("Computing dynamics...")
        transitivities = list(map(lambda x: nx.transitivity(x) / max_clustering, small_world_graphs))
        avg_lenghts = list(map(lambda x: nx.average_shortest_path_length(x) / max_length, small_world_graphs))  
        dynamics = list(map(lambda x: get_dynamics(x, params), small_world_graphs))
        
        
        transitivity.append(np.mean(transitivities))
        average_path_length.append(np.mean(avg_lenghts))
        dynamics_data[p] = dynamics

    # Save the data for each p
    data_ipr_rho = sum([list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values], [])
    data_ipr_O = sum([list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values], [])
    data_ipr_eigenvector = sum([list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values], [])
    data_variance_rho = sum([list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values], [])
    data_variance_O = sum([list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values], [])
    data_variance_eigenvector = sum([list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values], [])
    data_k_avg = sum([list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values], [])
    
    data_p = sum([[p] * sample_size for p in p_values], [])

    # Plot the results
    print("Plotting the results...")
    fig, axes = plt.subplots(5, 1, figsize=(10, 12))

    # Plot transitivity and average path length
    axes[0].plot(p_values, transitivity, label='Transitivity')
    axes[0].plot(p_values, average_path_length, label='Average Path Length')
    axes[0].set_xlabel('p')
    axes[0].set_xscale('log')
    axes[0].legend()
    axes[0].set_title('Transitivity and Average Path Length')
    axes[0].grid(True)

    # Plot dynamics: IPR
    axes[1].scatter(data_p, data_ipr_rho, label='IPR rho', alpha=0.7)
    axes[1].scatter(data_p, data_ipr_O, label='IPR O', alpha=0.7)
    axes[1].set_xlabel('p')
    axes[1].set_xscale('log')
    axes[1].legend()
    axes[1].set_title('Dynamics: IPR')
    axes[1].grid(True)

    # Plot variance
    axes[2].scatter(data_p, data_variance_rho, label='Variance rho', alpha=0.7)
    axes[2].scatter(data_p, data_variance_O, label='Variance O', alpha=0.7)
    axes[2].set_xlabel('p')
    axes[2].set_xscale('log')
    axes[2].legend()
    axes[2].set_title('Variance')
    axes[2].grid(True)

    # Plot IPR eigenvector
    axes[3].scatter(data_p, data_ipr_eigenvector, label='IPR eigenvector', alpha=0.7)
    axes[3].set_xlabel('p')
    axes[3].set_xscale('log')
    axes[3].legend()
    axes[3].set_title('IPR Eigenvector')
    axes[3].grid(True)

    # Plot variance eigenvector
    axes[4].scatter(data_p, data_variance_eigenvector, label='Variance eigenvector', alpha=0.7)
    axes[4].set_xlabel('p')
    axes[4].set_xscale('log')
    axes[4].legend()
    axes[4].set_title('Variance Eigenvector')
    axes[4].grid(True)

    plt.tight_layout()
    plt.show()

    return {
        "dynamics_data": dynamics_data,
        "data_ipr_rho": data_ipr_rho,
        "data_ipr_O": data_ipr_O,
        "data_ipr_eigenvector": data_ipr_eigenvector,
        "data_variance_rho": data_variance_rho,
        "data_variance_O": data_variance_O,
        "data_variance_eigenvector": data_variance_eigenvector,
        "data_k_avg": data_k_avg
    }
In [7]:
experiment = experiments(30, 6, 10, 2, params)
print(experiment)
Starting the experiments...
Computing graph 1/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 2/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 3/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 4/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 5/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 6/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 7/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 8/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 9/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Computing graph 10/10...
Computing samples...
Computing dynamics...
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Integration finished.
Linear algebra computations...
Computations finished.
Plotting the results...
No description has been provided for this image
{'dynamics_data': {np.float64(0.0001): [{'critical_eigenvalue': -2.2166138832471804, 'last_values_rho': [0.008069369484021295, 0.007757991823145214, 0.007793425361537228, 0.007848646375082624, 0.00780989513852471, 0.007910842841756038, 0.008021379685619084, 0.008095398401131403, 0.008191136477534697, 0.008217009270683206, 0.00818974370770322, 0.008087548342653987, 0.007922520014682726, 0.007845419749730924, 0.007639427228197823, 0.007451296886199155, 0.006811399902373398, 0.0056427017689586936, 0.007355472924916334, 0.007932542688189478, 0.007939240168919247, 0.007939501526918984, 0.007934794593733245, 0.007943088492244146, 0.007940227913686957, 0.007937463136890617, 0.00793674089393442, 0.0041482318525373554, 0.005807604486486839, 0.0069190259692731085], 'last_values_O': [0.6547344961459031, 0.6224460694396733, 0.6265632638216883, 0.6325340974268451, 0.6288520448208552, 0.6395144381491416, 0.6507461465356832, 0.6577757198745879, 0.6663127794936624, 0.6667269643972175, 0.6611952578592568, 0.6474986052385735, 0.6268898284572708, 0.6170037667518701, 0.5938887089899964, 0.5713386959357427, 0.5018836823072351, 0.3746958358646023, 0.5123677065827231, 0.6355728080343549, 0.6350081014428479, 0.6349870987914438, 0.6353755504226279, 0.6347024775252073, 0.6349289822788796, 0.6351524304587735, 0.6352119615281909, 0.2220301352213436, 0.40825445486338324, 0.5320480911525368], 'critical_eigenvector': [0.003512562286297117, -0.10180034588825296, -0.18951104943161556, -0.24445357087441705, -0.2571278491220584, -0.22534238632332013, -0.15459317775796771, -0.057113404323333526, 0.050241795577794665, 0.14890973259113857, 0.22182982403702273, 0.2563935236462212, 0.24662445375494937, 0.19421177529662195, 0.10821811653092007, 0.0035125622862969184, -0.10180034588825371, -0.18951104943161565, -0.24445357087441646, -0.25712784912205827, -0.22534238632331988, -0.1545931777579676, -0.057113404323333575, 0.050241795577794506, 0.14890973259113818, 0.2218298240370224, 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Experiments distributed¶

In [ ]:
from multiprocessing import Pool

def process_graph(args):
    """Helper function to process a single graph with given parameters"""
    p, seed, n_nodes, n_neighbors, params = args
    graph = nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed)
    max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
    max_length = n_nodes / (2 * n_neighbors)
    
    transitivity = nx.transitivity(graph) / max_clustering
    avg_length = nx.average_shortest_path_length(graph) / max_length
    
    dynamics = get_dynamics(graph, params)

    # Compute the measures for the random erdos renyi graph
    avg_degree = dynamics["k_avg"]
    transitivity_random = (avg_degree / n_nodes) / max_clustering
    avg_length_random = (np.log(n_nodes) / np.log(avg_degree)) / max_length
    sigma = (transitivity / transitivity_random) / (avg_length / avg_length_random)

    # Compute the presence of hubs
    max_degree = max(dict(graph.degree()).values())
    hub_ness = max_degree / avg_degree
    return {
        'transitivity': transitivity,
        'avg_length': avg_length,
        'dynamics': dynamics,
        'sigma': sigma,
        'hub_ness': hub_ness
    }

def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
    print("Starting the experiments...")
    transitivity = []
    average_path_length = []
    sigma_data = []
    hub_data = []
    p_values = np.logspace(-4, 0, n_experiments)
    dynamics_data = {}

    # Create process pool
    with Pool() as pool:
        for i, p in enumerate(p_values):
            print(f"Computing graph {i + 1}/{n_experiments}...")
            
            # Prepare arguments for parallel processing
            args = [(p, seed, n_nodes, n_neighbors, params) for seed in range(sample_size)]
            
            # Process graphs in parallel
            results = pool.map(process_graph, args)
            
            # Extract results
            transitivities = [r['transitivity'] for r in results]
            avg_lengths = [r['avg_length'] for r in results]
            dynamics = [r['dynamics'] for r in results]
            sigmas = [r['sigma'] for r in results]
            hubs = [r['hub_ness'] for r in results]
            
            transitivity.append(np.mean(transitivities))
            average_path_length.append(np.mean(avg_lengths))
            dynamics_data[p] = dynamics
            # Save the mean of sigma
            sigma_data.append(np.mean(sigmas))
            # Save the mean of hub_ness
            hub_data.append(np.mean(hubs))


    # Rest of the code remains the same
    data_ipr_rho = sum([list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values], [])
    data_ipr_O = sum([list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values], [])
    data_ipr_eigenvector = sum([list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values], [])
    data_variance_rho = sum([list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values], [])
    data_variance_O = sum([list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values], [])
    data_variance_eigenvector = sum([list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values], [])
    data_k_avg = sum([list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values], [])
    
    data_p = sum([[p] * sample_size for p in p_values], [])

    # Plot the results
    print("Plotting the results...")
    fig, axes = plt.subplots(5, 1, figsize=(10, 12))

    # Plot transitivity and average path length
    axes[0].plot(p_values, transitivity, label='Transitivity')
    axes[0].plot(p_values, average_path_length, label='Average Path Length')
    # Plot vertical line for small world condition when True
    axes[0].plot(p_values, sigma_data, label='Small-world-ness')
    axes[0].plot(p_values, hub_data, label='Hub-ness')
    axes[0].set_xlabel('p')
    axes[0].set_xscale('log')
    axes[0].legend()
    axes[0].set_title('Transitivity and Average Path Length')
    axes[0].grid(True)

    # Plot dynamics: IPR
    axes[1].scatter(data_p, data_ipr_rho, label='IPR rho', alpha=0.7)
    axes[1].scatter(data_p, data_ipr_O, label='IPR O', alpha=0.7)
    axes[1].set_xlabel('p')
    axes[1].set_xscale('log')
    axes[1].legend()
    axes[1].set_title('Dynamics: IPR')
    axes[1].grid(True)

    # Plot variance
    axes[2].scatter(data_p, data_variance_rho, label='Variance rho', alpha=0.7)
    axes[2].scatter(data_p, data_variance_O, label='Variance O', alpha=0.7)
    axes[2].set_xlabel('p')
    axes[2].set_xscale('log')
    axes[2].legend()
    axes[2].set_title('Variance')
    axes[2].grid(True)

    # Plot IPR eigenvector
    axes[3].scatter(data_p, data_ipr_eigenvector, label='IPR eigenvector', alpha=0.7)
    axes[3].set_xlabel('p')
    axes[3].set_xscale('log')
    axes[3].legend()
    axes[3].set_title('IPR Eigenvector')
    axes[3].grid(True)

    # Plot variance eigenvector
    axes[4].scatter(data_p, data_variance_eigenvector, label='Variance eigenvector', alpha=0.7)
    axes[4].set_xlabel('p')
    axes[4].set_xscale('log')
    axes[4].legend()
    axes[4].set_title('Variance Eigenvector')
    axes[4].grid(True)

    plt.tight_layout()
    plt.show()

    return {
        "dynamics_data": dynamics_data,
        "data_ipr_rho": data_ipr_rho,
        "data_ipr_O": data_ipr_O,
        "data_ipr_eigenvector": data_ipr_eigenvector,
        "data_variance_rho": data_variance_rho,
        "data_variance_O": data_variance_O,
        "data_variance_eigenvector": data_variance_eigenvector,
        "data_k_avg": data_k_avg
    }

Experiments distributed with box plots¶

In [23]:
from multiprocessing import Pool

def process_graph(args):
    """Helper function to process a single graph with given parameters"""
    p, seed, n_nodes, n_neighbors, params = args
    graph = nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed)
    max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
    max_length = n_nodes / (2 * n_neighbors)
    
    transitivity = nx.transitivity(graph) / max_clustering
    avg_length = nx.average_shortest_path_length(graph) / max_length
    
    dynamics = get_dynamics(graph, params)

    # Compute the measures for the random erdos renyi graph
    avg_degree = dynamics["k_avg"]
    transitivity_random = (avg_degree / n_nodes) / max_clustering
    avg_length_random = (np.log(n_nodes) / np.log(avg_degree)) / max_length
    sigma = (transitivity / transitivity_random) / (avg_length / avg_length_random)

    # Compute the presence of hubs
    max_degree = max(dict(graph.degree()).values())
    hub_ness = max_degree / avg_degree
    return {
        'transitivity': transitivity,
        'avg_length': avg_length,
        'dynamics': dynamics,
        'sigma': sigma,
        'hub_ness': hub_ness
    }

def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
    print("Starting the experiments...")
    transitivity = []
    average_path_length = []
    sigma_data = []
    hub_data = []
    p_values = np.logspace(-4, 0, n_experiments)
    dynamics_data = {}

    # Create process pool
    with Pool() as pool:
        for i, p in enumerate(p_values):
            print(f"Computing graph {i + 1}/{n_experiments}...")
            
            # Prepare arguments for parallel processing
            args = [(p, seed, n_nodes, n_neighbors, params) for seed in range(sample_size)]
            
            # Process graphs in parallel
            results = pool.map(process_graph, args)
            
            # Extract results
            transitivities = [r['transitivity'] for r in results]
            avg_lengths = [r['avg_length'] for r in results]
            dynamics = [r['dynamics'] for r in results]
            sigmas = [r['sigma'] for r in results]
            hubs = [r['hub_ness'] for r in results]
            
            transitivity.append(np.mean(transitivities))
            average_path_length.append(np.mean(avg_lengths))
            dynamics_data[p] = dynamics
            # Save the mean of sigma
            sigma_data.append(np.mean(sigmas))
            # Save the mean of hub_ness
            hub_data.append(np.mean(hubs))


    # Rest of the code remains the same
    data_ipr_rho = [list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values]
    data_ipr_O = [list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values]
    data_ipr_eigenvector = [list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values]
    data_variance_rho = [list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values]
    data_variance_O = [list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values]
    data_variance_eigenvector = [list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values]
    data_k_avg = [list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values]
    
    data_p = p_values

    # Plot the results
    print("Plotting the results...")
    fig, axes = plt.subplots(5, 1, figsize=(10, 12))

    # Plot transitivity and average path length
    axes[0].plot(p_values, transitivity, label='Transitivity')
    axes[0].plot(p_values, average_path_length, label='Average Path Length')
    # Plot vertical line for small world condition when True
    axes[0].plot(p_values, sigma_data, label='Small-world-ness')
    axes[0].plot(p_values, hub_data, label='Hub-ness')
    axes[0].set_xlabel('p')
    axes[0].set_xscale('log')
    axes[0].legend()
    axes[0].set_title('Transitivity and Average Path Length')
    axes[0].grid(True)

    # Plot dynamics: IPR
    widths = 0.1 * data_p
    # Plot dynamics: IPR (rho and O)
    for i, (x, y, w) in enumerate(zip(data_p, data_ipr_rho, widths)):
        if i == 0:
            axes[1].boxplot(y, positions=[x], widths=[w], label='IPR rho')
        else:
            axes[1].boxplot(y, positions=[x], widths=[w])
    for i, (x, y, w) in enumerate(zip(data_p, data_ipr_O, widths)):
        if i == 0:
            axes[1].boxplot(y, positions=[x], widths=[w], label='IPR O')
        else:
            axes[1].boxplot(y, positions=[x], widths=[w])
    axes[1].set_xlabel('p')
    axes[1].set_xscale('log')
    axes[1].legend()
    axes[1].set_title('Dynamics: IPR')
    axes[1].grid(True)

    # Plot variance (rho and O) as boxplots
    for i, (x, y, w) in enumerate(zip(data_p, data_variance_rho, widths)):
        if i == 0:
            axes[2].boxplot(y, positions=[x], widths=[w], label='Variance rho')
        else:
            axes[2].boxplot(y, positions=[x], widths=[w])
    for i, (x, y, w) in enumerate(zip(data_p, data_variance_O, widths)):
        if i == 0:
            axes[2].boxplot(y, positions=[x], widths=[w], label='Variance O')
        else:
            axes[2].boxplot(y, positions=[x], widths=[w])
    axes[2].set_xlabel('p')
    axes[2].set_xscale('log')
    axes[2].legend()
    axes[2].set_title('Variance')
    axes[2].grid(True)

    # Plot IPR eigenvector as boxplots
    for i, (x, y, w) in enumerate(zip(data_p, data_ipr_eigenvector, widths)):
        if i == 0:
            axes[3].boxplot(y, positions=[x], widths=[w], label='IPR eigenvector')
        else:
            axes[3].boxplot(y, positions=[x], widths=[w])
    axes[3].set_xlabel('p')
    axes[3].set_xscale('log')
    axes[3].legend()
    axes[3].set_title('IPR Eigenvector')
    axes[3].grid(True)

    # Plot variance eigenvector as boxplots
    for i, (x, y, w) in enumerate(zip(data_p, data_variance_eigenvector, widths)):
        if i == 0:
            axes[4].boxplot(y, positions=[x], widths=[w], label='Variance eigenvector')
        else:
            axes[4].boxplot(y, positions=[x], widths=[w])
    axes[4].set_xlabel('p')
    axes[4].set_xscale('log')
    axes[4].legend()
    axes[4].set_title('Variance Eigenvector')
    axes[4].grid(True)

    plt.tight_layout()
    plt.show()

    return {
        "dynamics_data": dynamics_data,
        "data_ipr_rho": data_ipr_rho,
        "data_ipr_O": data_ipr_O,
        "data_ipr_eigenvector": data_ipr_eigenvector,
        "data_variance_rho": data_variance_rho,
        "data_variance_O": data_variance_O,
        "data_variance_eigenvector": data_variance_eigenvector,
        "data_k_avg": data_k_avg
    }
In [24]:
experiment = experiments(16, 4, 50, 8, params)
print(experiment)
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Computations finished.
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Starting the integration...

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Linear algebra computations...Linear algebra computations...

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Starting the integration...
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Integration finished.
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Computations finished.Computations finished.

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Starting the integration...

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Integration finished.
Computations finished.Integration finished.Linear algebra computations...


Linear algebra computations...
Computations finished.
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Linear algebra computations...
Computations finished.
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Starting the integration...

Starting the integration...Starting the integration...



Computing graph 26/50...
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Integration finished.Computations finished.

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Linear algebra computations...Integration finished.

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Starting the integration...Starting the integration...

Computing graph 27/50...
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Linear algebra computations...Linear algebra computations...

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Computing graph 29/50...
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Computing graph 30/50...
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Computing graph 31/50...
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Computing graph 32/50...
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Computing graph 33/50...
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Computing graph 34/50...
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Integration finished.
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Computing graph 35/50...
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Linear algebra computations...
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Computations finished.
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Starting the integration...
Computing graph 36/50...
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Linear algebra computations...Computations finished.

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Linear algebra computations...Linear algebra computations...

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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 37/50...
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Integration finished.Computations finished.
Integration finished.Computations finished.


Linear algebra computations...Linear algebra computations...

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Starting the integration...






Computing graph 38/50...
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Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

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Starting the integration...






Computing graph 39/50...
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 40/50...
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Linear algebra computations...Integration finished.

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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 41/50...
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Linear algebra computations...
Computations finished.Integration finished.Integration finished.


Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 42/50...
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Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...


Computations finished.Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
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Starting the integration...

Computing graph 43/50...
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Integration finished.
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Integration finished.
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Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 44/50...
Integration finished.
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Linear algebra computations...Linear algebra computations...

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Integration finished.
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Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 45/50...
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
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Linear algebra computations...
Linear algebra computations...

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Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 46/50...
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6522442301296834
Integration finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.Linear algebra computations...

Computations finished.Integration finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. -2.4908803515668563
Integration finished.
Linear algebra computations...

/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Linear algebra computations...Computations finished.

Computations finished.
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 47/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
-1.7763568394002505e-15Linear algebra computations...

/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.Computations finished.

Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6896803071991684
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.829489310684999
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 48/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Integration finished.
Linear algebra computations...Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The linear analysis cannot be performed.

The critical eigenvalue is:  The critical eigenvalue is: Integration finished. -1.7763568394002505e-150.0


Linear algebra computations...Computations finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
8.881784197001252e-16Linear algebra computations...
Integration finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations...


The linear analysis cannot be performed.
The critical eigenvalue is: Computations finished.Integration finished. 

-3.552713678800501e-15Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6645352591003757e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 49/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  3.552713678800501e-15Integration finished.

Linear algebra computations...Computations finished.

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  7.105427357601002e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations...

The linear analysis cannot be performed.
The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: 
 The linear analysis cannot be performed.-1.7763568394002505e-15

The critical eigenvalue is: Computations finished. 
-8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -3.552713678800501e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.5670163022740397e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 50/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
Integration finished.The linear analysis cannot be performed.

Linear algebra computations...
The critical eigenvalue is:  The critical eigenvalue is not in the range of the dispersion relation.2.6645352591003757e-15

Computations finished.The linear analysis cannot be performed.

The critical eigenvalue is:  0.0Integration finished.

Computations finished.Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.The critical eigenvalue is not in the range of the dispersion relation.

Linear algebra computations...The linear analysis cannot be performed.

The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation. 
5.329070518200751e-15The linear analysis cannot be performed.

Computations finished.The critical eigenvalue is: 
 1.7763568394002505e-15
Integration finished.Computations finished.

Linear algebra computations...Integration finished.

Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation.

The critical eigenvalue is: The linear analysis cannot be performed. 
1.7763568394002505e-15The critical eigenvalue is: 
 Computations finished.0.0

/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Plotting the results...
No description has been provided for this image
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0.06250000000000001, 0.0625, 0.06249999999999999, 0.0625, 0.0625], [0.0625, 0.06250000000000001, 0.0625, 0.06250000000000001, 0.0625, 0.06249999999999999, 0.0625, 0.0625], [0.0625, 0.06250000000000001, 0.0625, 0.06250000000000001, 0.0625, 0.062499999999999986, 0.0625, 0.062499999999999986], [0.0625, 0.06250000000000001, 0.0625, 0.06249999999999999, 0.062499999999999986, 0.062499999999999986, 0.0625, 0.0625], [0.0625, 0.06250000000000001, 0.0625, 0.06249999999999999, 0.06249999999999999, 0.062499999999999986, 0.0625, 0.062499999999999986], [0.06250000000000001, 0.0625, 0.0625, 0.06249999999999999, 0.062499999999999986, 0.062499999999999986, 0.0625, 0.062499999999999986], [0.06250000000000001, 0.0625, 0.0625, 0.06249999999999999, 0.06250000000000001, 0.062499999999999986, 0.0625, 0.062499999999999986], [0.06250000000000001, 0.0625, 0.0625, 0.06250000000000001, 0.06250000000000001, 0.0625, 0.0625, 0.06249999999999998], [0.06250000000000001, 0.0625, 0.06250000000000001, 0.06250000000000001, 0.0625, 0.062499999999999986, 0.0625, 0.062499999999999986], [0.06250000000000001, 0.0625, 0.06250000000000001, 0.0625, 0.0625, 0.0625, 0.0625, 0.062499999999999986], [0.062499999999999986, 0.0625, 0.062499999999999986, 0.0625, 0.062499999999999986, 0.0625, 0.06249999999999999, 0.062499999999999986], [0.06250000000000001, 0.0625, 0.062499999999999986, 0.06249999999999999, 0.0625, 0.0625, 0.06250000000000001, 0.062499999999999986], [0.062499999999999986, 0.06249999999999999, 0.0625, 0.0625, 0.0625, 0.0625, 0.0625, 0.0625], [0.0625, 0.0625, 0.062499999999999986, 0.062499999999999986, 0.0, 0.0625, 0.0625, 0.0], [0.0, 0.0, 0.06249999999999999, 0.062499999999999986, 0.0, 0.06249999999999999, 0.0625, 0.0], [0.0, 0.0, 0.0625, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.25, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.25, 4.0, 4.125, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.25, 4.125, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.5, 4.125, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.5, 4.125, 4.25, 4.0, 4.25, 4.25, 4.125], [4.0, 4.5, 4.125, 4.375, 4.0, 4.25, 4.25, 4.125], [4.0, 4.5, 4.25, 4.375, 4.0, 4.5, 4.25, 4.5], [4.0, 4.5, 4.25, 4.375, 4.25, 4.5, 4.25, 4.625], [4.0, 4.5, 4.25, 4.375, 4.375, 4.5, 4.25, 4.75], [4.125, 4.625, 4.25, 4.375, 4.5, 4.5, 4.625, 5.0], [4.125, 4.625, 4.25, 4.375, 4.75, 4.5, 4.625, 5.0], [4.125, 5.0, 4.25, 4.75, 4.75, 4.75, 4.625, 5.125], [4.125, 5.0, 4.625, 4.75, 4.75, 5.0, 4.625, 5.375], [4.125, 5.0, 4.625, 5.0, 4.875, 5.125, 5.0, 5.375], [5.0, 5.125, 4.5, 5.0, 5.5, 5.375, 4.75, 5.375], [5.125, 5.125, 4.75, 5.0, 5.5, 5.75, 5.0, 5.375], [5.5, 5.125, 5.25, 5.125, 5.5, 5.875, 5.25, 5.5], [5.375, 5.5, 5.25, 5.375, 6.125, 5.875, 5.375, 6.375], [6.5, 6.25, 5.625, 5.75, 6.625, 6.0, 6.25, 6.75], [6.75, 6.75, 6.0, 6.375, 7.0, 6.625, 7.0, 7.125], [7.125, 7.375, 7.125, 7.5, 7.625, 7.375, 7.625, 7.625], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0]]}
In [23]:
experiment_2 = experiments(25, 6, 50, 8, params)
print(experiment_2)
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...




Starting the integration...

Computing graph 26/50...
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Linear algebra computations...Computations finished.

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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 27/50...
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Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
Integration finished.
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Computations finished.
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Starting the integration...






Computing graph 28/50...
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 29/50...
Integration finished.Integration finished.

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Linear algebra computations...
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Integration finished.Computations finished.

Linear algebra computations...
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Linear algebra computations...
Computations finished.
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Linear algebra computations...
Computations finished.
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Starting the integration...


Computing graph 30/50...
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Integration finished.
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Integration finished.
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Computations finished.
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Computations finished.
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Starting the integration...
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Computations finished.
Integration finished.
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Computations finished.
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Computations finished.
Integration finished.Integration finished.

Integration finished.Linear algebra computations...Linear algebra computations...

Linear algebra computations...

Integration finished.Computations finished.

Computations finished.Linear algebra computations...Computations finished.


Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 32/50...
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Linear algebra computations...
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Linear algebra computations...
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Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 33/50...
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Linear algebra computations...Integration finished.

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Linear algebra computations...
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Computations finished.
Integration finished.
Linear algebra computations...
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Linear algebra computations...
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Starting the integration...
Computing graph 34/50...
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Integration finished.
Linear algebra computations...Integration finished.Integration finished.


Computations finished.Linear algebra computations...Linear algebra computations...


Computations finished.Computations finished.

Integration finished.
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 35/50...
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Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
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Computations finished.
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Linear algebra computations...
Computations finished.
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Starting the integration...





Computing graph 36/50...
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Integration finished.
Linear algebra computations...
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Computations finished.
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
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Computing graph 37/50...
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Linear algebra computations...
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Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 38/50...
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Integration finished.
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Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
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Starting the integration...






Computing graph 39/50...
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Integration finished.
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Integration finished.Computations finished.

Linear algebra computations...
Integration finished.
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Computations finished.
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Starting the integration...






Computing graph 40/50...
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Computations finished.
Integration finished.
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Linear algebra computations...
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Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 41/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
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Linear algebra computations...
Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...






Computing graph 42/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
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Integration finished.
Linear algebra computations...
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Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.185771349294377
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 43/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.5381982318695693
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 44/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
Integration finished.The linear analysis cannot be performed.

Linear algebra computations...The critical eigenvalue is: 
 -2.4207140732126824The critical eigenvalue is not in the range of the dispersion relation.

/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
The linear analysis cannot be performed.Computations finished.

The critical eigenvalue is:  -2.589536457801767
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.Integration finished.


Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 45/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
Integration finished.The critical eigenvalue is: 
 Linear algebra computations...-2.5124816146229656

/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.281055244917911
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.Integration finished.
The linear analysis cannot be performed.

Linear algebra computations...The critical eigenvalue is: 
 -2.4578211740250353The critical eigenvalue is not in the range of the dispersion relation.

Computations finished.The linear analysis cannot be performed.

The critical eigenvalue is:  -2.5739038435598554
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
Integration finished.The critical eigenvalue is: 
 Linear algebra computations...-8.881784197001252e-16

The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The linear analysis cannot be performed.Integration finished.


The critical eigenvalue is: Linear algebra computations... 
-2.462970217952612
The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The linear analysis cannot be performed.

The critical eigenvalue is:  8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.3322676295501878e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...




Computing graph 46/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  Integration finished.1.7763568394002505e-15

Linear algebra computations...Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished.
 8.881784197001252e-16Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.Integration finished.

The critical eigenvalue is: Linear algebra computations... 
-8.881784197001252e-16
The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
The linear analysis cannot be performed.Computations finished.

The critical eigenvalue is:  0.0
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.047129243061654e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6645352591003757e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 47/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed.

The linear analysis cannot be performed.The critical eigenvalue is: 
 The critical eigenvalue is: -1.3322676295501878e-15 
-8.881784197001252e-16Computations finished.

Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: 
 The linear analysis cannot be performed.0.0

The critical eigenvalue is: Computations finished. 
-8.881784197001252e-16
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 48/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.041714481980183e-15
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation.

The critical eigenvalue is: The linear analysis cannot be performed. 0.0

The critical eigenvalue is: Computations finished. 
8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -3.552713678800501e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.220446049250313e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.509817662595573e-16
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 49/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.915748542778049e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The linear analysis cannot be performed.

The critical eigenvalue is: The critical eigenvalue is:   3.552713678800501e-151.7763568394002505e-15

Computations finished.Computations finished.

Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed.

The linear analysis cannot be performed.The critical eigenvalue is: 
 The critical eigenvalue is: -1.2690089419017577e-15 
3.552713678800501e-15Computations finished.

Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations...

The linear analysis cannot be performed.
The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: 
 The linear analysis cannot be performed.-1.7763568394002505e-15

The critical eigenvalue is: Computations finished. 
-2.6645352591003757e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...

Starting the integration...Starting the integration...



Computing graph 50/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.Integration finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.The critical eigenvalue is: 
 The critical eigenvalue is: -8.881784197001252e-16 
-2.8222448992052524e-15Computations finished.

Integration finished.Computations finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The linear analysis cannot be performed.

The critical eigenvalue is: The critical eigenvalue is:   0.0-9.292183877208547e-16

Computations finished.Computations finished.

Plotting the results...
No description has been provided for this image
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0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001], [0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001], [0.039999999999999994, 0.04, 0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04, 0.04, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04, 0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.04], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.039999999999999994], [0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04], [0.04000000000000001, 0.04, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.040000000000000015, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.04, 0.039999999999999994, 0.039999999999999994, 0.0, 0.039999999999999994, 0.04, 0.04000000000000001], [0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.0, 0.04, 0.04, 0.04000000000000001], [0.04000000000000001, 0.04, 0.03999999999999999, 0.0, 0.0, 0.0, 0.04, 0.04000000000000001], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.16, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.24, 6.0, 6.08, 6.0, 6.24, 6.24, 6.0], [6.08, 6.24, 6.08, 6.08, 6.0, 6.24, 6.24, 6.0], [6.16, 6.4, 6.08, 6.24, 6.0, 6.24, 6.32, 6.0], [6.16, 6.4, 6.08, 6.24, 6.0, 6.24, 6.32, 6.08], [6.16, 6.4, 6.08, 6.32, 6.16, 6.24, 6.32, 6.08], [6.16, 6.4, 6.16, 6.32, 6.16, 6.4, 6.32, 6.24], [6.24, 6.4, 6.16, 6.88, 6.4, 6.56, 6.32, 6.48], [6.24, 6.64, 6.16, 6.88, 6.56, 6.56, 6.32, 6.8], [6.8, 6.88, 6.16, 6.88, 6.64, 6.56, 6.64, 7.12], [6.72, 6.88, 6.16, 7.04, 6.88, 7.04, 6.72, 7.28], [6.8, 6.88, 6.16, 7.28, 6.96, 7.12, 6.72, 7.28], [6.8, 6.88, 6.48, 7.36, 6.96, 7.2, 6.96, 7.28], [6.88, 7.12, 6.48, 7.52, 7.44, 7.6, 7.2, 7.44], [7.52, 7.28, 6.64, 7.84, 7.6, 7.76, 7.44, 7.52], [7.44, 7.36, 6.88, 8.24, 8.16, 8.16, 7.68, 8.08], [8.08, 7.84, 7.68, 8.4, 8.8, 8.8, 8.48, 8.4], [8.64, 8.48, 8.32, 8.88, 9.04, 9.36, 8.96, 9.44], [9.12, 9.52, 8.8, 9.6, 9.44, 9.36, 9.6, 10.16], [9.84, 9.92, 10.08, 10.24, 10.08, 10.32, 10.0, 10.64], [10.48, 11.04, 10.8, 10.64, 11.2, 11.12, 11.12, 11.2], [12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0]]}
In [25]:
experiment_3 = experiments(40, 8, 50, 8, params)
print(experiment_3)
Starting the experiments...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...





Starting the integration...
Computing graph 1/50...
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),

/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
Computations finished.
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),

/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Computing graph 2/50...
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Integration finished.Linear algebra computations...

Linear algebra computations...Computations finished.

Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),

/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 3/50...
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.
Linear algebra computations...

Computations finished.Integration finished.

Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 4/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Integration finished.Computations finished.


Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...




Computing graph 5/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...





Computing graph 6/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...





Computing graph 7/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Integration finished.Computations finished.


Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 8/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...





Computing graph 9/50...
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 10/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...





Computing graph 11/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...

Starting the integration...


Computing graph 12/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 13/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 14/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 15/50...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
Computations finished.
Computations finished.
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Starting the integration...

Starting the integration...Starting the integration...




Computing graph 16/50...
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Linear algebra computations...
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
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Computing graph 17/50...
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Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
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Computing graph 18/50...
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Computations finished.Integration finished.

Linear algebra computations...
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Computing graph 19/50...
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Computations finished.
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Starting the integration...Starting the integration...



Computing graph 20/50...
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Integration finished.Linear algebra computations...

Linear algebra computations...
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Integration finished.
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Starting the integration...
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Starting the integration...


Computing graph 21/50...
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Starting the integration...Starting the integration...
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Computing graph 22/50...
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Computations finished.
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Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...




Computing graph 23/50...
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Linear algebra computations...Computations finished.

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Linear algebra computations...
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Computing graph 24/50...
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Starting the integration...Starting the integration...


Starting the integration...


Starting the integration...
Computing graph 25/50...
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Starting the integration...




Computing graph 26/50...
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Computations finished.
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Starting the integration...
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Starting the integration...



Computing graph 27/50...
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 28/50...
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Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...




Computing graph 29/50...
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...

Computing graph 30/50...
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Linear algebra computations...Linear algebra computations...

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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...Starting the integration...Starting the integration...



Computing graph 31/50...
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Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Integration finished.
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Starting the integration...Starting the integration...






Computing graph 32/50...
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Linear algebra computations...
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Computations finished.
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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 33/50...
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Computations finished.
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 34/50...
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Integration finished.
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Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 35/50...
Integration finished.
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Computations finished.
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Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...





Computing graph 36/50...
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Integration finished.
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Integration finished.
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Computations finished.
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 37/50...
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Integration finished.
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Computations finished.
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Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
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Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 38/50...
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
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Integration finished.
Linear algebra computations...Computations finished.

Computations finished.
Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...





Computing graph 39/50...
Integration finished.
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Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

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Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...
Starting the integration...Starting the integration...




Computing graph 40/50...
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
Integration finished.
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Linear algebra computations...
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...





Computing graph 41/50...
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
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Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...





Computing graph 42/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.407968440118764
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.3169223386273403
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...




Starting the integration...
Computing graph 43/50...
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
-2.4972330430819487
Linear algebra computations...
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.272325315368397
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.2548615863376638
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.68406466817104
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.4340214168083305
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.2882658402642044
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 44/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.8265810535668106
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.Linear algebra computations...

The critical eigenvalue is:  The critical eigenvalue is not in the range of the dispersion relation.-2.58979352102367

The linear analysis cannot be performed.Computations finished.

The critical eigenvalue is:  -2.777485888506203
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.3322676295501878e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.7995255566177097
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.3322676295501878e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
4.440892098500626e-16Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 45/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  Integration finished.
8.881784197001252e-16Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.3322676295501878e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.7763568394002505e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.Integration finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  5.810106010205084e-16
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 46/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
-1.5044397281716031e-15Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -3.552713678800501e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
4.440892098500626e-16Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.7763568394002505e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...





Computing graph 47/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.0567257790018154e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -3.2125298715835343e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.8754757027629315e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.0676877769707976e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...





Computing graph 48/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.6630936661505222e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -6.168085144480596e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.8374154189959897e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.6645352591003757e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7232489678676572e-15
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation.

The critical eigenvalue is: The linear analysis cannot be performed. 
9.705552083232977e-16The critical eigenvalue is: 
 Computations finished.-8.881784197001252e-16

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...




Computing graph 49/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.7865462195338268e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  3.1079364088969327e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.0128582962932408e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.7698237345273254e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is: Integration finished. 
8.881784197001252e-16Linear algebra computations...

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -3.4120797654081527e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...
Starting the integration...




Computing graph 50/50...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.8118598154984204e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.1397156435696196e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  6.580620990714174e-15Integration finished.

Computations finished.Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -4.808412112914714e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.227648577984641e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -5.807892406662716e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  5.57723272274762e-16
Computations finished.
Plotting the results...
No description has been provided for this image
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(-9.537345462622156+0j), (-9.53734546262216+0j), (-9.509525449494415+0j), (-9.50952544949444+0j), (-8.237242708226779+0j), (-8.237242708226791+0j), (-8.726208811623659+0j), (-8.726208811623655+0j), (-8.879191113239036+0j), (-8.87919111323906+0j), (-8.841615559675445+0j), (-8.841615559675468+0j), (-10.000000000000004+0j), (-10+0j), (-10.000000000000007+0j), (-7.999999999999987+0j), (-7.999999999999997+0j), (-7.999999999999999+0j), (-8+0j), (-9.999999999999996+0j), (-10.000000000000002+0j), (-9.999999999999995+0j), (-7.999999999999996+0j), (-8+0j), (-7.999999999999998+0j), (-9.999999999999995+0j), (-10.000000000000002+0j)], 'variance_rho': 4.855475511230553e-08, 'variance_O': 0.0015433058835536396, 'variance_eigenvector': 0.025000000000000012, 'ipr_rho': 0.025070657351797653, 'ipr_O': 0.02536002715631172, 'ipr_eigenvector': 0.037500000000000006, 'k_avg': 8.0}, {'critical_eigenvalue': -0.7224632490927867, 'last_values_rho': [0.007912260481837212, 0.007912556224662274, 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0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000005, 0.025, 0.025, 0.025000000000000005], [0.025, 0.024999999999999994, 0.025000000000000012, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005], [0.024999999999999998, 0.024999999999999998, 0.025000000000000012, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.02499999999999999, 0.025000000000000005], [0.025, 0.024999999999999994, 0.025, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005], [0.024999999999999998, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994], [0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994, 0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994], [0.025, 0.024999999999999998, 0.025000000000000005, 0.024999999999999994, 0.025000000000000005, 0.024999999999999994, 0.025, 0.024999999999999994], [0.025, 0.025000000000000005, 0.025, 0.024999999999999994, 0.025, 0.025, 0.025, 0.025], [0.025, 0.025000000000000005, 0.02499999999999999, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025, 0.025], [0.025, 0.025000000000000005, 0.025, 0.025000000000000005, 0.025, 0.025, 0.025, 0.025], [0.024999999999999994, 0.025000000000000005, 0.025, 0.025, 0.025, 0.025, 0.025, 0.025000000000000005], [0.025, 0.025000000000000005, 0.025, 0.025, 0.025, 0.02499999999999999, 0.024999999999999994, 0.024999999999999994], [0.024999999999999994, 0.025, 0.024999999999999994, 0.025000000000000005, 0.025, 0.025000000000000005, 0.025, 0.02499999999999999], [0.025, 0.025, 0.025, 0.025, 0.024999999999999998, 0.024999999999999998, 0.024999999999999994, 0.025], [0.025000000000000005, 0.025, 0.025000000000000005, 0.024999999999999994, 0.025, 0.025, 0.024999999999999998, 0.024999999999999998], [0.025000000000000012, 0.024999999999999994, 0.025, 0.024999999999999998, 0.025, 0.024999999999999998, 0.025000000000000005, 0.025000000000000005], [0.025, 0.025, 0.024999999999999998, 0.025, 0.0, 0.025, 0.024999999999999994, 0.0], [0.025, 0.0, 0.0, 0.0, 0.0, 0.024999999999999994, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.15, 8.0, 8.0, 8.05, 8.05, 8.05, 8.1], [8.1, 8.2, 8.0, 8.1, 8.05, 8.1, 8.05, 8.1], [8.1, 8.25, 8.0, 8.1, 8.05, 8.1, 8.1, 8.1], [8.1, 8.25, 8.05, 8.1, 8.1, 8.1, 8.2, 8.1], [8.2, 8.3, 8.15, 8.15, 8.1, 8.2, 8.3, 8.1], [8.25, 8.3, 8.3, 8.2, 8.1, 8.2, 8.3, 8.1], [8.3, 8.5, 8.4, 8.25, 8.1, 8.25, 8.3, 8.1], [8.3, 8.55, 8.45, 8.25, 8.2, 8.35, 8.3, 8.1], [8.25, 8.55, 8.7, 8.4, 8.3, 8.35, 8.3, 8.1], [8.25, 8.55, 8.7, 8.4, 8.4, 8.5, 8.3, 8.25], [8.45, 8.55, 8.7, 8.45, 8.65, 8.75, 8.3, 8.55], [8.7, 8.6, 8.7, 8.45, 8.8, 8.8, 8.4, 8.7], [8.9, 8.8, 8.7, 8.6, 8.75, 8.85, 8.7, 8.85], [8.95, 9.0, 8.85, 8.75, 8.95, 9.2, 8.85, 9.3], [9.05, 9.05, 9.15, 9.15, 9.0, 9.4, 8.95, 9.4], [9.15, 9.15, 9.45, 9.3, 9.4, 9.5, 9.35, 9.55], [9.35, 9.65, 9.55, 9.5, 9.75, 9.55, 9.6, 9.9], [9.75, 9.95, 10.15, 9.95, 10.25, 9.7, 10.1, 10.0], [10.1, 10.4, 10.7, 10.9, 11.15, 10.65, 10.7, 10.3], [11.05, 10.85, 11.05, 11.15, 11.7, 11.15, 11.05, 10.9], [11.3, 11.7, 11.7, 12.15, 12.35, 11.5, 11.85, 12.0], [12.35, 12.55, 12.3, 12.65, 12.85, 12.25, 12.5, 12.85], [13.6, 13.6, 13.15, 13.5, 13.95, 13.3, 13.1, 13.5], [14.3, 14.7, 14.7, 14.4, 14.65, 14.55, 15.05, 14.75], [16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0]]}
In [24]:
experiment_4 = experiments(60, 8, 100, 8, params)
print(experiment_4)
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Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Starting the integration...
Computing graph 21/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.Integration finished.

Linear algebra computations...
Linear algebra computations...
Computations finished.
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 22/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
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Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 23/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...
Starting the integration...Starting the integration...Starting the integration...




Computing graph 24/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...Starting the integration...Starting the integration...

Starting the integration...

Computing graph 25/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 26/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...
Starting the integration...




Computing graph 27/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...





Computing graph 28/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...






Computing graph 29/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...


Starting the integration...

Computing graph 30/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...






Computing graph 31/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...



Computing graph 32/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...



Computing graph 33/100...
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...Computations finished.

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...




Computing graph 34/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 35/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Integration finished.Linear algebra computations...


Linear algebra computations...
Computations finished.Computations finished.

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...Starting the integration...
Starting the integration...



Computing graph 36/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...





Computing graph 37/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...Starting the integration...

Starting the integration...


Computing graph 38/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...





Computing graph 39/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Integration finished.Computations finished.

Linear algebra computations...
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...



Starting the integration...Starting the integration...

Starting the integration...
Computing graph 40/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...
Starting the integration...Starting the integration...



Computing graph 41/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Starting the integration...Starting the integration...Starting the integration...

Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...
Starting the integration...


Computing graph 42/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...




Computing graph 43/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...Starting the integration...Starting the integration...




Computing graph 44/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...Starting the integration...

Computing graph 45/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Integration finished.
Computations finished.Linear algebra computations...


Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...


Starting the integration...


Computing graph 46/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 47/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 48/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...
Starting the integration...

Starting the integration...Starting the integration...


Computing graph 49/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...Starting the integration...Starting the integration...
Starting the integration...



Computing graph 50/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...

Starting the integration...Starting the integration...
Starting the integration...



Computing graph 51/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 52/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.Integration finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...

Starting the integration...
Starting the integration...

Starting the integration...
Computing graph 53/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...
Starting the integration...Starting the integration...Starting the integration...



Computing graph 54/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...Starting the integration...




Computing graph 55/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Starting the integration...Starting the integration...Starting the integration...


Starting the integration...
Computing graph 56/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...




Starting the integration...
Starting the integration...
Computing graph 57/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...Computations finished.

Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...



Computing graph 58/100...
Integration finished.
Linear algebra computations...
Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part
  'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part
  'ipr_eigenvector': float(ipr_eigenvector),
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...
Starting the integration...


Starting the integration...


Computing graph 59/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...


Starting the integration...
Starting the integration...

Computing graph 60/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...Integration finished.

Linear algebra computations...
Computations finished.
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
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Computations finished.
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Computing graph 82/100...
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Linear algebra computations...
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Linear algebra computations...Linear algebra computations...

Computations finished.Computations finished.

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Computations finished.
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Starting the integration...Starting the integration...

Computing graph 86/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.246823104399011
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
Integration finished.
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Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
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Computations finished.
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Starting the integration...
Starting the integration...

Starting the integration...
Starting the integration...
Computing graph 87/100...
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.5393647463732294
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.545918372139427
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.1652201325005853
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...

Starting the integration...Starting the integration...
Starting the integration...



Computing graph 88/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.2591066991801916
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.3676975114945655
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Computations finished.Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.4768759452845495
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.457538677667931
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...

Starting the integration...Starting the integration...Starting the integration...



Computing graph 89/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.529875503227853
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.4395505121558343
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.3157374346599044
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6929750101459025
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.Computations finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.3560011292923596e-15
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 90/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
Integration finished.
The linear analysis cannot be performed.Linear algebra computations...
The critical eigenvalue is: 
 1.3322676295501878e-15
Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.7631972248629397
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.8117702911145477
Computations finished.
Integration finished.
Linear algebra computations...
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  5.917350894406997e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...Starting the integration...






Computing graph 91/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.440892098500626e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.184989577114578
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.4982417285529586
Computations finished.
Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...
Starting the integration...




Computing graph 92/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
Integration finished.
The linear analysis cannot be performed.Linear algebra computations...

The critical eigenvalue is:  0.0
The critical eigenvalue is not in the range of the dispersion relation.Computations finished.

The linear analysis cannot be performed.
The critical eigenvalue is:  1.3322676295501878e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -5.656712314709048e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -5.0180997951793105e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.377710667796089e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...







Computing graph 93/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.234351599827366e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -5.2889700095621834e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.9051493342871517e-15
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.
The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: 
 The linear analysis cannot be performed.-4.440892098500626e-16

The critical eigenvalue is: Computations finished. 
-8.881784197001252e-16
Computations finished.
Integration finished.
Integration finished.Linear algebra computations...

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed.

The linear analysis cannot be performed.The critical eigenvalue is: 
 The critical eigenvalue is: 0.0 
8.881784197001252e-16Computations finished.

Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...





Starting the integration...
Computing graph 94/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  3.3164948617519065e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.1539287319758375e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.0007570361716873e-15
Computations finished.
Starting the integration...Starting the integration...

Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...





Computing graph 95/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6645352591003757e-15
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations...

The linear analysis cannot be performed.
The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation. 
1.7763568394002505e-15The linear analysis cannot be performed.

Computations finished.The critical eigenvalue is: 
 -2.6645352591003757e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.963710006122749e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...





Computing graph 96/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.7763568394002505e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.129302624024876e-15
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.
The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations...

The linear analysis cannot be performed.
The critical eigenvalue is:  The critical eigenvalue is not in the range of the dispersion relation.-1.7763568394002505e-15

The linear analysis cannot be performed.
Computations finished.The critical eigenvalue is: 
 3.3981721674106285e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  3.0341378075920944e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.285693916740988e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -1.1101265337434621e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.403836223964361e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...
Starting the integration...

Starting the integration...
Starting the integration...



Computing graph 97/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -4.970809807355093e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.0540052542774768e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  0.0
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.509429278524096e-15
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The linear analysis cannot be performed.

The critical eigenvalue is: The critical eigenvalue is:   -6.565892017633031e-16-5.40972761303715e-15

Computations finished.
Computations finished.
Starting the integration...Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...

Starting the integration...

Computing graph 98/100...
Starting the integration...


Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.4496634653628537e-15
Computations finished.
Integration finished.
Linear algebra computations...
Integration finished.The critical eigenvalue is not in the range of the dispersion relation.

Linear algebra computations...
The linear analysis cannot be performed.
The critical eigenvalue is:  The critical eigenvalue is not in the range of the dispersion relation.0.0

The linear analysis cannot be performed.Computations finished.

The critical eigenvalue is:  1.0067009351638022e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  8.881784197001252e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
Integration finished.The critical eigenvalue is: 
 Linear algebra computations...-3.364222517974507e-15

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.8199062527937e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.2079864686876847e-15
Computations finished.
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...


Starting the integration...
Starting the integration...



Computing graph 99/100...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  3.552713678800501e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.Integration finished.
The critical eigenvalue is: 
 Linear algebra computations...1.7763568394002505e-15

Computations finished.
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  1.0113397725625435e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.1476787684794742e-15
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.Integration finished.

The linear analysis cannot be performed.Linear algebra computations...

The critical eigenvalue is:  -4.178887069980057e-15
The critical eigenvalue is not in the range of the dispersion relation.
Computations finished.The linear analysis cannot be performed.

The critical eigenvalue is:  -1.0561632216261665e-15Integration finished.

Computations finished.Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  4.176751134223985e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -9.374678378614101e-16
Computations finished.
Starting the integration...Starting the integration...Starting the integration...


Starting the integration...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...



Computing graph 100/100...
Integration finished.Integration finished.

Linear algebra computations...
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.

The linear analysis cannot be performed.The critical eigenvalue is: Integration finished.

 Linear algebra computations...The critical eigenvalue is: 3.552713678800501e-15
 -4.17364950999942e-15

Computations finished.The critical eigenvalue is not in the range of the dispersion relation.
Computations finished.
The linear analysis cannot be performed.

The critical eigenvalue is:  -2.273002726061519e-16
Computations finished.
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -8.881784197001252e-16
Integration finished.Computations finished.

Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  5.329070518200751e-15
Computations finished.
Integration finished.Integration finished.

Linear algebra computations...Linear algebra computations...

The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation.

The linear analysis cannot be performed.The linear analysis cannot be performed.

The critical eigenvalue is: The critical eigenvalue is:   4.516563007987751e-15-3.3988684354622447e-16

Computations finished.Computations finished.

Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -9.70043214339077e-16
Computations finished.
Plotting the results...
No description has been provided for this image
{'dynamics_data': {np.float64(0.0001): [{'critical_eigenvalue': -1.2603186817795815, 'last_values_rho': [0.007913275673366504, 0.0079137213698872, 0.00792086863887327, 0.007924633443712513, 0.007927862752940728, 0.007932827348254883, 0.007938302369854327, 0.00794229008751715, 0.007945491981655678, 0.007948526881856427, 0.007949197868726953, 0.007948800901346063, 0.007949489665583776, 0.007950013804775908, 0.007944957387392268, 0.007942828303165117, 0.007892622434129571, 0.00775142662833852, 0.007537730023815444, 0.008237539975774312, 0.00793977740265393, 0.00794000730297712, 0.007935757027423385, 0.007943123227857556, 0.007940643476611388, 0.007938197841319366, 0.00793754648010574, 0.007942902660335854, 0.007938944271039451, 0.007940397393264324, 0.007943632170682089, 0.007939758658543484, 0.0079414870322974, 0.00793882931621006, 0.007938710277047591, 0.007934940509819962, 0.007933925871180983, 0.007939842590447492, 0.00794265257199038, 0.007942564812461167, 0.007940253310958214, 0.007940087576149538, 0.007939499173482424, 0.007941063170088518, 0.00793451074075059, 0.00793838035083013, 0.007939408594538368, 0.007942151625815299, 0.007941100083474272, 0.007939386562085409, 0.007938637745149978, 0.007933071884329318, 0.00793957473418727, 0.007937045825563682, 0.007936974881342807, 0.007936091984258603, 0.00667479308068001, 0.00730650612726805, 0.00787937012535416, 0.007944477422582984], 'last_values_O': [0.6299072168589803, 0.6302667047891902, 0.6314431572478988, 0.632159034544702, 0.6327890646603264, 0.6337935131182982, 0.6348645962533298, 0.6357433720235517, 0.6365149037356663, 0.6372578367654388, 0.6376691672345467, 0.6379108339439926, 0.6381866640495945, 0.6384394747672796, 0.6379688752236574, 0.637858009340745, 0.6311229979092906, 0.6104220761182837, 0.573115633551028, 0.7321577439645882, 0.6349638093566686, 0.6349456571752515, 0.6352813932410281, 0.6346997372461181, 0.6348954321563369, 0.635088552030704, 0.6351400045066155, 0.6347171384880191, 0.6350295987701557, 0.6349148591780828, 0.6346595893219633, 0.6349652893736862, 0.634828846786693, 0.6350386773101964, 0.6350480786532982, 0.6353459250067783, 0.6354261287854496, 0.6349586622413373, 0.6347368700154191, 0.6347437944115377, 0.6349262342775333, 0.6349393192981736, 0.634985778725582, 0.634862302225034, 0.6353798949709781, 0.6350741364838923, 0.634992931270477, 0.6347763978759923, 0.6348593885080187, 0.6349946710819998, 0.6350538071179885, 0.6354936448293836, 0.634979812205956, 0.6351795571284087, 0.6351851621844139, 0.6352549236259516, 0.3927027810992685, 0.5338513685142627, 0.6241134106670698, 0.6338275617683183], 'critical_eigenvector': [0.0020534520300776885, -0.03594832749886753, -0.07237899261689823, -0.1056463484446302, -0.13429645189790723, -0.1570771559773716, -0.17299283460080447, -0.18134789624046205, -0.18177718461065778, -0.17426193774965984, -0.15913060800744996, -0.13704450710193725, -0.1089689036235642, -0.07613083616602748, -0.039965485851752816, -0.0020534520300782362, 0.03594832749886724, 0.07237899261689786, 0.10564634844463024, 0.13429645189790723, 0.15707715597737176, 0.17299283460080453, 0.181347896240462, 0.18177718461065817, 0.1742619377496601, 0.1591306080074498, 0.1370445071019375, 0.10896890362356403, 0.07613083616602792, 0.03996548585175285, 0.0020534520300779673, -0.035948327498867186, -0.07237899261689815, -0.10564634844463024, -0.13429645189790732, -0.15707715597737174, -0.17299283460080467, -0.18134789624046252, -0.18177718461065778, -0.17426193774966015, -0.15913060800744977, -0.13704450710193702, -0.10896890362356387, -0.07613083616602788, -0.039965485851752774, -0.002053452030078031, 0.03594832749886726, 0.07237899261689852, 0.10564634844463036, 0.13429645189790723, 0.15707715597737165, 0.1729928346008042, 0.18134789624046208, 0.18177718461065814, 0.17426193774965992, 0.15913060800744971, 0.13704450710193722, 0.10896890362356385, 0.07613083616602759, 0.03996548585175241], 'eigenvalues': [6.248738990912598e-16, -0.32545705992033264, -0.3254570599203305, -1.2603186817795748, -1.2603186817795815, -2.686248485324957, -6.26794919243111, -2.6862484853249624, -4.425670809782484, -4.425670809782498, -6.26794919243113, -10.999999999999977, -10.999999999999996, -10.962610505505157, -10.962610505505165, -10.635957885691777, -10.635957885691774, -7.729082579618058, -7.729082579618056, -7.720227223967837, -7.720227223967806, -10.44512490403513, -10.445124904035078, -8.107770706574033, -8.107770706574012, -8.458678392814303, -8.408977062214593, -8.40897706221457, -8.4586783928143, -8.538181348396984, -8.538181348397014, -8.841615559675466, -8.841615559675457, -9.0, -9.00000000000001, -9.885579351970744, -10.057957421302163, -10.057957421302142, -9.885579351970739, -9.732050807568873, -9.73205080756888, -9.436519128562454, -9.509525449494436, -9.509525449494433, -9.436519128562464, -9.248576825516897, -9.248576825516915, -9.31592061785267, -9.315920617852688, -7.999999999999995, 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0.016666666666666666], [0.0, 0.0, 0.01666666666666667, 0.0, 0.0, 0.0, 0.01666666666666667, 0.016666666666666666], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01666666666666666, 0.016666666666666666], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.016666666666666666, 0.016666666666666666], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.0, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333], [8.066666666666666, 8.0, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.066666666666666, 8.066666666666666, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333, 8.066666666666666], [8.1, 8.066666666666666, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333, 8.1], [8.1, 8.066666666666666, 8.0, 8.0, 8.033333333333333, 8.033333333333333, 8.033333333333333, 8.1], [8.1, 8.066666666666666, 8.033333333333333, 8.033333333333333, 8.066666666666666, 8.033333333333333, 8.066666666666666, 8.1], [8.1, 8.066666666666666, 8.066666666666666, 8.033333333333333, 8.066666666666666, 8.1, 8.066666666666666, 8.1], [8.1, 8.066666666666666, 8.066666666666666, 8.033333333333333, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.066666666666666, 8.066666666666666, 8.033333333333333, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.066666666666666, 8.066666666666666, 8.033333333333333, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.066666666666666, 8.066666666666666, 8.066666666666666, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.1, 8.066666666666666, 8.066666666666666, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.166666666666666, 8.066666666666666, 8.066666666666666, 8.1, 8.1, 8.066666666666666, 8.1], [8.1, 8.166666666666666, 8.066666666666666, 8.066666666666666, 8.1, 8.1, 8.1, 8.1], [8.1, 8.166666666666666, 8.066666666666666, 8.033333333333333, 8.1, 8.1, 8.1, 8.1], [8.1, 8.166666666666666, 8.066666666666666, 8.033333333333333, 8.1, 8.1, 8.1, 8.1], [8.166666666666666, 8.166666666666666, 8.066666666666666, 8.1, 8.1, 8.1, 8.1, 8.1], 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[8.266666666666667, 8.4, 8.5, 8.333333333333334, 8.133333333333333, 8.266666666666667, 8.366666666666667, 8.2], [8.266666666666667, 8.433333333333334, 8.566666666666666, 8.333333333333334, 8.266666666666667, 8.266666666666667, 8.366666666666667, 8.2], [8.266666666666667, 8.5, 8.566666666666666, 8.333333333333334, 8.333333333333334, 8.266666666666667, 8.4, 8.2], [8.266666666666667, 8.5, 8.633333333333333, 8.533333333333333, 8.4, 8.266666666666667, 8.4, 8.2], [8.333333333333334, 8.5, 8.633333333333333, 8.533333333333333, 8.4, 8.266666666666667, 8.4, 8.266666666666667], [8.333333333333334, 8.5, 8.633333333333333, 8.633333333333333, 8.5, 8.333333333333334, 8.4, 8.266666666666667], [8.433333333333334, 8.566666666666666, 8.766666666666667, 8.633333333333333, 8.5, 8.366666666666667, 8.433333333333334, 8.266666666666667], [8.433333333333334, 8.566666666666666, 8.766666666666667, 8.7, 8.733333333333333, 8.433333333333334, 8.533333333333333, 8.333333333333334], [8.433333333333334, 8.633333333333333, 8.833333333333334, 8.766666666666667, 8.733333333333333, 8.566666666666666, 8.533333333333333, 8.466666666666667], [8.7, 8.666666666666666, 8.9, 8.733333333333333, 8.866666666666667, 8.566666666666666, 8.533333333333333, 8.466666666666667], [8.9, 8.733333333333333, 8.9, 8.8, 8.933333333333334, 8.566666666666666, 8.633333333333333, 8.533333333333333], [8.933333333333334, 8.7, 8.9, 8.8, 8.9, 8.7, 8.733333333333333, 8.7], [9.033333333333333, 8.9, 9.133333333333333, 8.933333333333334, 8.966666666666667, 8.7, 8.8, 8.8], [9.033333333333333, 9.1, 9.133333333333333, 8.933333333333334, 9.0, 8.866666666666667, 8.8, 8.8], [9.033333333333333, 9.1, 9.233333333333333, 9.133333333333333, 9.1, 8.9, 8.966666666666667, 8.966666666666667], [9.133333333333333, 9.3, 9.3, 9.3, 9.166666666666666, 8.966666666666667, 9.0, 9.2], [9.133333333333333, 9.3, 9.333333333333334, 9.366666666666667, 9.266666666666667, 9.133333333333333, 9.0, 9.4], [9.2, 9.4, 9.433333333333334, 9.5, 9.533333333333333, 9.233333333333333, 9.366666666666667, 9.6], [9.3, 9.4, 9.6, 9.6, 9.566666666666666, 9.366666666666667, 9.5, 9.7], [9.566666666666666, 9.433333333333334, 9.733333333333333, 9.733333333333333, 9.666666666666666, 9.5, 9.6, 9.966666666666667], [9.633333333333333, 9.766666666666667, 9.966666666666667, 9.866666666666667, 9.733333333333333, 9.566666666666666, 9.8, 10.0], [9.666666666666666, 9.8, 10.1, 9.966666666666667, 9.866666666666667, 9.566666666666666, 10.0, 10.1], [10.166666666666666, 9.933333333333334, 10.4, 10.266666666666667, 10.3, 9.933333333333334, 10.1, 10.133333333333333], [10.7, 10.233333333333333, 10.433333333333334, 10.2, 10.7, 10.3, 10.4, 10.2], [10.966666666666667, 10.566666666666666, 10.7, 10.733333333333333, 10.933333333333334, 10.633333333333333, 10.533333333333333, 10.333333333333334], [11.333333333333334, 10.766666666666667, 10.833333333333334, 10.833333333333334, 11.133333333333333, 11.0, 10.6, 10.5], [11.7, 11.266666666666667, 11.266666666666667, 11.133333333333333, 11.4, 11.166666666666666, 10.733333333333333, 10.7], [11.8, 11.633333333333333, 11.4, 11.666666666666666, 11.866666666666667, 11.366666666666667, 11.233333333333333, 11.066666666666666], [12.1, 12.0, 11.9, 12.233333333333333, 12.1, 11.6, 12.1, 12.133333333333333], [12.266666666666667, 12.233333333333333, 12.166666666666666, 12.3, 12.233333333333333, 11.866666666666667, 12.5, 12.4], [12.6, 12.733333333333333, 12.466666666666667, 12.7, 12.666666666666666, 12.233333333333333, 12.766666666666667, 12.666666666666666], [13.133333333333333, 12.933333333333334, 12.9, 13.2, 13.133333333333333, 13.0, 13.1, 13.166666666666666], [13.366666666666667, 13.4, 13.266666666666667, 13.566666666666666, 13.666666666666666, 13.5, 13.533333333333333, 13.466666666666667], [13.966666666666667, 13.633333333333333, 13.933333333333334, 14.233333333333333, 13.966666666666667, 14.066666666666666, 14.033333333333333, 14.033333333333333], [14.466666666666667, 14.566666666666666, 14.6, 14.7, 14.466666666666667, 14.666666666666666, 14.566666666666666, 14.566666666666666], [15.2, 15.166666666666666, 15.1, 15.366666666666667, 15.333333333333334, 15.266666666666667, 15.166666666666666, 15.233333333333333], [16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0]]}

Antes del cambio de fase¶

In [25]:
# Generate a small world graph with p=0.3 
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)

graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.01, seed=40)

# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.01 (Circular Layout)")
plt.show()
No description has been provided for this image
In [ ]:
# # Create an empty graph
# G = nx.Graph()

# # Add nodes
# nodes = range(1, 17)
# G.add_nodes_from(nodes)

# # Add edges based on the visual structure
# edges = [
#     (1, 2), (1, 3), (1, 4), (2, 4), (2,5), (3, 4), (3, 6), (3, 7), (3, 8), (4, 5), (4, 8), (4, 9),
#     (5, 9), (6, 7), (7, 8), (7, 11), (7, 10), (7, 13), (8, 9), (8, 11), (8, 12), (9, 12),
#     (10, 13), (11, 12), (11, 13), (11, 14), (12, 14), (12, 15), (13, 14), (13, 16) ,(14, 15),
#     (14, 16), (15, 16)
# ]
# G.add_edges_from(edges)
# graph = G
In [15]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration...
Integration finished.
Linear algebra computations...
No description has been provided for this image
Computations finished.

Justo en el cambio de fase¶

In [ ]:
# Generate a small world graph with p=0.3 
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)

# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.3 (Circular Layout)")
plt.show()
No description has been provided for this image
In [21]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  2.220446049250313e-15
No description has been provided for this image
Computations finished.
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)

Después del cambio de fase¶

In [18]:
# Generate a small world graph with p=0.3 
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.8, seed=40)

# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.3 (Circular Layout)")
plt.show()
No description has been provided for this image
In [19]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration...
Integration finished.
Linear algebra computations...
The critical eigenvalue is not in the range of the dispersion relation.
The linear analysis cannot be performed.
The critical eigenvalue is:  -2.6645352591003757e-15
No description has been provided for this image
Computations finished.
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide
  ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)